{"id":382,"date":"2012-08-07T14:33:42","date_gmt":"2012-08-07T06:33:42","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=382"},"modified":"2012-08-09T22:09:16","modified_gmt":"2012-08-09T14:09:16","slug":"spoj-11470-to-the-moon","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/spoj-11470-to-the-moon\/","title":{"rendered":"SPOJ 11470. To the moon"},"content":{"rendered":"

Brief description: <\/h3>\n

\u52a8\u6001\u7ef4\u62a4\u5e8f\u5217\uff0c\u8981\u6c42\u652f\u6301\u533a\u95f4\u589e\u51cf\uff0c\u5386\u53f2\u533a\u95f4\u8be2\u95ee\uff0c\u4ee5\u53ca\u56de\u6863\u5230\u67d0\u4e2a\u5386\u53f2\u72b6\u6001\u3002\u3002
\n\uff08\u3002\u3002\u56de\u6863\u540e\u4e0d\u53ef\u8fd4\u56de\u3002\u3002\u3002<\/p>\n

<\/p>\n

Tucao: <\/h3>\n

\u3002\u3002\u561b\u3002\u3002\u9898\u76ee\u51fa\u6210\u8fd9\u6837\u6211\u4e5f\u6ca1\u4ec0\u4e48\u597d\u8fa9\u89e3\u7684\u4e86\u3002\u3002
\n\u539f\u672c\u7684\u9898\u76ee\u8fd8\u6709\u4e00\u4e2a retroact \u64cd\u4f5c\u3002\u3002\u5141\u8bb8\u5bf9\u4e00\u4e2a\u5386\u53f2\u7684\u8be2\u95ee\u505a\u4fee\u6539\u3002\u3002\u7136\u540e\u56de\u5230\u73b0\u5b9e\u770b\u770b\u53d1\u751f\u4e86\u54ea\u4e9b\u53d8\u5316\u3002\u3002
\n\u800c\u4e14\u5f3a\u5236\u5728\u7ebf\u3002\u3002\u8fd9\u6837\u7684\u8bdd\u662f\u3002\u3002\u90e8\u5206\u53ef\u6301\u4e45\u5316\u6761\u4ef6\u4e0b\u7684\u4e00\u9636\u8ffd\u6714\u6027\u6570\u636e\u7ed3\u6784\u3002\u3002
\n\u4e00\u822c\u60c5\u51b5\u4e0b\u597d\u50cf\u6ca1\u6cd5\u505a\u3002\u3002\u4f46\u662f\u5728\u64cd\u4f5c\u540c\u65f6\u5177\u6709\u6ee1\u8db3\u9006\u64cd\u4f5c\u5b58\u5728\u3001\u548c\u4ea4\u6362\u5f8b\u7684\u60c5\u51b5\u4e0b\u3002\u3002\u53ef\u4ee5\u7528\u4e3b\u5e2d\u6811\u7ef4\u62a4\u3002\u3002\u3002<\/p>\n

\u3002\u3002\u4e0d\u8fc7\u540e\u6765\u53d1\u73b0\u8fd9\u4e2a\u4e1c\u897f\u7b49\u4ef7\u4e8e\u4e00\u4e2a\u4e8c\u7ef4\u7684\u7ebf\u6bb5\u6811\u95ee\u9898\u3002\u3002\u3002\u89c9\u5f97\u6ca1\u4ec0\u4e48\u610f\u601d\u3002\u3002\u5c31\u53bb\u6389\u4e86\u3002\u3002\u3002
\n\u3002\u3002\u3002\u4e8e\u662f\u5c31\u53d8\u5f97\u6bd4\u8f83\u4fdd\u5b88\u3002\u3002\u800c\u4e14\u60f3\u5230\u53bb\u5e74\u7684\u9898\u76ee<\/a>\u8fd8\u9632\u4e86 AK \u3002\u3002\u6240\u4ee5\u8fd9\u6b21\u672c\u6765\u4e5f\u662f\u3002\u3002\u60f3\u51fa\u4e00\u9053\u666e\u901a\u7a0b\u5ea6\u7684\u9898\u3002\u3002
\n\uff08\u3002\u3002\u6700\u8fd1\u5728\u8bfb \u300aokasaki\u300b\u3002\u3002\u53d1\u73b0\u53d1\u73b0\u53bb\u5e74\u90a3\u53ea\u9898\u76ee\u7684\u65b9\u6cd5\u5c45\u7136\u6709\u540d\u5b57\u7684\u3002\u3002\uff08\u3002\u3002\u3002 Global Reconstruction\u3002\u3002\u3002<\/p>\n

\u3002\u3002\uff08\u3002\u3002\u7136\u540e\u4e4b\u524d\u4ee5\u4e3a\u662f\u4e0b\u4e2a\u661f\u671f\u4e8c\u591a\u6821\u3002\u3002\u6240\u4ee5\u5348\u7761\u7684\u65f6\u5019\u88ab\u53eb\u9192\u4e86\u3002\u3002\u3002\u4e0a\u6765\u770b\u4e86\u4e00\u4e0b\u53d1\u73b0 hud \u7684\u9898\u76ee\u63cf\u8ff0\u5c45\u7136\u7c98\u9519\u4e86\u3002\u3002
\n\u3002\u660e\u660e\u5728 Hoj \u548c Spoj \u90fd\u662f\u6392\u7248\u597d\u4e86\u7684\u554a\u3002\u3002\u800c\u4e14\u5c45\u7136\u662f HIT \u4e13\u573a\u3002\u3002\u3002\u672c\u6765\u50cf\u662f 1011 \u8fd9\u79cd\u9898\u3002\u3002\u5c31\u4e0d\u53ef\u80fd\u5e94\u8be5\u8ba9\u5b83\u51fa\u73b0\u5728\u591a\u6821\u4e4b\u4e2d\uff01\u3002\u3002\u6211\u4e5f\u53ea\u662f\u9a8c\u4e86\u81ea\u5df1\u7684\u9898\u76ee\u3002\u3002\u4e2d\u95f4\u8854\u63a5\u7684\u8fc7\u7a0b\u4e5f\u505a\u7684\u5f88\u4e0d\u597d\u3002\u3002\u975e\u5e38\u62b1\u6b49\uff01\u3002\u3002\u3002\u3002\u3002<\/p>\n

Analysis: <\/h3>\n

\u672c\u9898\u8003\u67e5\u53ef\u6301\u4e45\u5316\u6570\u636e\u7ed3\u6784\uff0c\u53ef\u6301\u4e45\u5316\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u4f9d\u636e\u9700\u6c42\uff0c\u53ef\u5206\u4e3a\u3002\u3002<\/p>\n

1. Partially persistent \uff08\u90e8\u5206\u6301\u4e45\u5316\uff09
\n \u5141\u8bb8\u5bf9\u5386\u53f2\u67e5\u8be2\uff0c\u4f46\u662f\u53ea\u80fd\u5bf9\u5f53\u524d\u7248\u672c\u8fdb\u884c\u4fee\u6539\u3002
\n \u7528\u56fe\u8bba\u672f\u8bed\u63cf\u8ff0\u5373\u662f\u7ebf\u6027\u7ed3\u6784\u3002\u3002<\/p>\n

2. Fully persistent (\u5b8c\u5168\u6301\u4e45\u5316)
\n \u5728\u90e8\u5206\u6301\u4e45\u5316\u7684\u57fa\u7840\u4e0a\uff0c\u652f\u6301\u5728\u5386\u53f2\u7248\u672c\u4e0a\u4fee\u6539\u3002
\n \u5373\u662f\u6811\u5f62\u7ed3\u6784\u3002\u3002\u3002<\/p>\n

3. Confluently persistent \uff08\u6c47\u805a\u6301\u4e45\u5316\uff09
\n \u5728\u5b8c\u5168\u6301\u4e45\u5316\u7684\u57fa\u7840\u4e0a\uff0c\u5141\u8bb8\u7528\u4e24\u4e2a\uff08\u6216\u591a\u4e2a\uff09\u5386\u53f2\u7248\u672c\u5f62\u6210\u4e00\u4e2a\u65b0\u7ed3\u70b9\u3002\u3002
\n \u56fe\u8bba\u63cf\u8ff0\u5373\u4e3a DAG \u3002\u3002\u3002
\nhttp:\/\/en.wikipedia.org\/wiki\/Persistent_data_structure<\/a><\/p>\n

\u3002\u3002\uff08SGI STL \u4e2d\u7684 Rope \uff08\u91cd\u7ef3\uff09\u5c31\u662f\u7b2c\u4e09\u79cd\u5f62\u6001\u7684\u4e00\u4e2a\u4f8b\u5b50\u3002\u3002
\n\u3002\u3002\uff08\u53e6\u5916\u6839\u636e Erik Demaine \u7684\u8bf4\u6cd5\u8fd8\u5b58\u5728\u7740\u66f4\u4e00\u822c\u7684 Functional persistent (\u51fd\u6570\u5f0f\u6301\u4e45\u5316)…
\nhttp:\/\/fanhq666.blog.163.com\/blog\/static\/81943426201161095456671\/<\/a>
\nhttp:\/\/ocw.mit.edu\/courses\/electrical-engineering-and-computer-science\/6-851-advanced-data-structures-spring-2010\/lecture-notes\/<\/a><\/p>\n

\u3002\u3002\u672c\u9898\u662f\u4ecb\u4e8e\u7b2c 1 \u7c7b\u548c\u7b2c 2 \u7c7b\u4e4b\u95f4\u7684\u5f62\u6001\u3002\u3002\u90e8\u5206\u6301\u4e45\u5316\uff0c
\n\u3002\u3002\u7136\u540e\u5141\u8bb8\u56de\u6863\u5230\u67d0\u4e2a\u5386\u53f2\u72b6\u6001\u3002\u3002\uff08\u4f46\u4e0d\u8981\u6c42\u76f4\u63a5\u4ece\u5386\u53f2\u72b6\u6001\u5904\u4fee\u6539\u3002\u3002\u3002<\/p>\n

\u5728\u7ebf\u505a\u6cd5\uff1a<\/p>\n

1. \u5e26\u6807\u8bb0\u7684\u4e3b\u5e2d\u6811\uff08\u3002\u4ee5 “Path Copying” \u65b9\u5f0f\u5b9e\u73b0\u7684\u7ebf\u6bb5\u6811\u3002\u3002<\/p>\n

\u3002O(logN) \u8be2\u95ee\u3001O(1) \u56de\u6863\u3002\u3002\u53e6\u5916\u4e3b\u5e2d\u6811\u672c\u8eab\u662f Fully persistent \u7684\u3002\u3002\u3002
\n \u3002\u3002\u4f46\u662f\u7a7a\u95f4\u590d\u6742\u5ea6 O(mlogn) \u4e14\u5e38\u6570\u8f83\u9ad8\u3002\u3002\u6bd4\u8f83\u5403\u5185\u5b58\u3002\u3002<\/p>\n

\uff08\u3002\u5177\u4f53\u53c2\u89c1\u9648\u4e3d\u6d01\u7684\u8bfe\u4ef6\u3002\u3002
\nhttp:\/\/hi.baidu.com\/wjbzbmr\/blog\/item\/a7f4a5996c328b95c9eaf489.html<\/a><\/p>\n

2. \u201c\u4e3b\u5e2d\u6570\u7ec4”\uff08\u4ee5 “Fat Node” \u65b9\u5f0f\u5b9e\u73b0\u7684\u6811\u72b6\u6570\u7ec4\u3002\u3002\u3002<\/p>\n

\u3002\u3002\u6811\u72b6\u6570\u7ec4\u7684\u6bcf\u4e2a\u7ed3\u70b9\u7ef4\u62a4\u4e00\u4e2a\u8bb0\u5f55\u65f6\u95f4\u6233\u7684\u6808\uff0c
\n \u8be2\u95ee\u65f6\u904d\u5386\u5230\u6bcf\u4e2a\u7ed3\u70b9\u518d\u4e8c\u5206\u67e5\u627e\u3002\u3002 O(nlog^2n) \u8be2\u95ee\u3002\u3002\u3002\u3002
\n \u7a7a\u95f4\u590d\u6742\u5ea6 O(mlogn)\u3002\u3002<\/p>\n

(\u5bf9\u4e8e\u56de\u6863\u64cd\u4f5c\u3002\u3002\u6211\u4eec\u4f7f\u7528\u66b4\u529b\u5f39\u6808\u3002\u3002
\n \u6bcf\u4e2a\u7ed3\u70b9\u81f3\u591a\u88ab\u5f39\u51fa\u4e00\u6b21\uff0c\u603b\u5171 O(nlogn) \u4e2a\u7ed3\u70b9\u3002\u3002\u3002 <\/p>\n

\u79bb\u7ebf\u505a\u6cd5\uff1a <\/p>\n

\u3002\u3002\u5806\u7ef4\u62a4\u8be2\u95ee\uff08\u6216\u8005\u76f4\u63a5\u63d2\u5230\u76f8\u5e94\u65f6\u523b\u7684\u94fe\u8868\u91cc\u3002\u3002)\u3002\u3002\u3002 \u6808\u7ef4\u62a4\u64cd\u4f5c\u3002\u3002\u6bcf\u6b21\u9047\u5230\u56de\u6863\u64cd\u4f5c\uff0c\u5219\u5f39\u51fa\u6240\u6709\u81f3\u6b64\u65f6\u523b\u7684\u8be2\u95ee\u3002\u3002
\n\u3002\u6700\u540e\u518d\u5f39\u5230 0 \u65f6\u523b\u5373\u53ef\u3002\u3002\u6bcf\u4e2a\u64cd\u4f5c\u5165\u6808\u51fa\u6808\u5404\u4e00\u6b21\u3002\u3002
\n\u3002\u3002\u8be2\u95ee\u590d\u6742\u5ea6 O(nlogn)\u3002\u3002\u7a7a\u95f4\u590d\u6742\u5ea6 O(nlogn)\u3002\u3002<\/p>\n

\u5e26\u6807\u8bb0\u7684\u4e3b\u5e2d\u6811\u3002\u3002\uff0812s+-\u3002\u3002\u3002110 M \u5185\u5b58\u3002\u3002<\/a>
\n\u4e3b\u5e2d\u6570\u7ec4\uff0817s+-\u3002\u3002\u3002<\/a>
\n\u79bb\u7ebf\u7b97\u6cd5\uff085s+-\u3002\u3002\u3002<\/a><\/p>\n

\uff08\u9884\u8ba1 AC \u961f\u4f0d\u4f1a\u6709 9~19 \u652f\uff1f\u3002\u3002\u800c\u4e14\u6bd4\u8d5b\u7684\u8bdd\u5927\u6982\u90fd\u662f\u4f1a\u5199\u8fd9\u79cd\u79bb\u7ebf\u7b97\u6cd5\u7684\u5427 ~\u3002\u3002\u3002<\/p>\n

External link: <\/h3>\n

http:\/\/www.spoj.pl\/problems\/TTM\/<\/a>
\nhttps:\/\/www.shuizilong.com\/house\/archives\/poj-3468-a-simple-problem-with-integers\/\uff08\u3002\u88f8\u9898\u3002\u3002\u6d4b\u6a21\u677f\u7528\u3002<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Brief description: \u52a8\u6001\u7ef4\u62a4\u5e8f\u5217\uff0c\u8981\u6c42\u652f\u6301\u533a\u95f4\u589e\u51cf\uff0c\u5386\u53f2\u533a\u95f4\u8be2\u95ee\uff0c\u4ee5\u53ca\u56de\u6863\u5230\u67d0\u4e2a\u5386\u53f2\u72b6\u6001\u3002\u3002 \uff08\u3002\u3002\u56de\u6863\u540e\u4e0d\u53ef\u8fd4\u56de\u3002\u3002\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[21],"tags":[78],"class_list":["post-382","post","type-post","status-publish","format-standard","hentry","category-spoj","tag-78"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-6a","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=382"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/382\/revisions"}],"predecessor-version":[{"id":383,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/382\/revisions\/383"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}